Q: If from any point on the circle x^{2} + y^{2} = a^{2} tangents are drawn to the circle x^{2} + y^{2} = a^{2} sin^{2} α , then the angle between the tangents, is

(A) α/2

(B) α

(C) 2α

(D) 4α

Sol:

The two given circles are concentric.

From figure, OP = a, OA = a sinα

If 2θ is the angle between the tangents,

$ sin\theta = \frac{a sin\alpha}{a} $

⇒ θ = α

Required angle between PA and PB = 2 α

Hence (C) is the correct answer.